A quantum system constrained to a degenerate energy eigenspace can undergo a nontrivial time evolution upon adiabatic driving, described by a non-Abelian Berry phase. This type of dynamics may provide logical gates in quantum computing that are robust against timing errors. A strong candidate to realize such holonomic quantum gates is an electron or hole spin qubit trapped in a spin-orbit-coupled semiconductor, whose twofold Kramers degeneracy is protected by time-reversal symmetry. In this talk, I propose and quantitatively analyze protocols to measure the non-Abelian Berry phase by pumping a spin qubit through a loop of quantum dots [1]. One of these protocols allows us to characterize the local internal Zeeman field directions in the dots of the loop. The near-term realisation of these protocols is expected, as all key elements have been already demonstrated in spin-qubit experiments. These experiments would be important to assess the potential of holonomic quantum gates for spin-based quantum information processing.

 

[1]: B. Kolok and A. Pályi: "Protocols to measure the non-Abelian Berry phase by pumping a spin qubit through a quantum-dot loop",  arXiv:2308.05455 (2023)